Black-Litterman and Markowitz Model Results Comparison Discussion

  TODO: Paragraphs to compare BL / Markowitz model results.



VIX Model Discussion  

  TODO: Paragraphs to discuss underperformance of VIX models (either rolling window or expanding window)




Turnover Ratio Discussion
  
TODO: Paragraph on how turnover ratio minimization helped/hurt portfolio returns

  While the motivation behind calculating TR is understood, we find the definition and methodology to be flawed. Recall the following definition:
  
\begin{equation}
TR(t+1)= \frac{\sum_{i=1}^6{|P_{i,t+1} - P_{i,t}|}}{\sum_{i=1}^6{|P_{i,t+1}|}}
\end{equation}

TR includes profits and loses as part of the turnover ratio. Spurious estimates of TR may be calculated even if asset weights remain the same. For example, a portfolio that never reallocates the distribution of capital between asets may have a high turnover ratio if it incurs a large profit or loss. Therefore, an estimate of turnover ratio related to changes in asset weights within a portfolio alone and not due to profit or losses attributable to market price fluctuation needs to be considered for a more accurate measure of transaction costs.
